How to find p value given coefficient and standard error?
The p value is a statistical measure that helps determine the significance of a coefficient or a parameter estimate in a statistical model. It tells us the probability of observing a coefficient as extreme as the one we have, assuming the null hypothesis is true (i.e., there is no relationship). To find the p value given a coefficient and standard error, we can follow these steps:
1. Identify the null hypothesis: The null hypothesis usually states that there is no relationship between the predictor variable and the outcome variable.
2. Calculate the t statistic: To find the t statistic, divide the coefficient by its standard error. The formula is: t = coefficient / standard error.
3. Determine the degrees of freedom: The degrees of freedom depend on the sample size and the number of predictors in the model. In general, the degrees of freedom are equal to the sample size minus the number of predictors.
4. Find the p value: Look up the t statistic in a t-distribution table or use software (such as statistical packages or calculators) to find the corresponding p value. The p value represents the probability of observing a t statistic as extreme as the one obtained, assuming the null hypothesis is true.
5. Interpret the p value: A p value below a predetermined threshold (usually 0.05) suggests that the coefficient is statistically significant. This means that the relationship between the predictor and outcome variables is unlikely to occur by chance alone.
It is important to note that the p value is not an indicator of the size or magnitude of the relationship. It only tells us about the statistical significance of the relationship.
FAQs:
1. What does a low p value indicate?
A low p value (below the predetermined threshold, usually 0.05) indicates that the coefficient is statistically significant. This suggests that the relationship between the predictor and outcome variables is unlikely to occur by chance alone.
2. Can the p value be greater than 1?
No, the p value cannot be greater than 1. It represents a probability and therefore ranges from 0 to 1.
3. What does a high p value indicate?
A high p value (above the predetermined threshold) indicates that the coefficient is not statistically significant. This suggests that the observed relationship between the predictor and outcome variables could plausibly occur by chance alone.
4. How does the sample size affect the p value?
Larger sample sizes tend to result in smaller p values, as they provide more precise estimates of the population parameters.
5. Can a significant coefficient have a high p value?
No, a significant coefficient is accompanied by a low p value. A high p value indicates that the coefficient is not statistically significant.
6. What is the relationship between the t statistic and the p value?
The t statistic is used to calculate the p value. It represents the number of standard errors the coefficient is away from zero. The p value represents the probability of observing a t statistic as extreme as the one obtained.
7. What if the p value is exactly 0?
A p value of exactly 0 implies that the observed coefficient is highly unlikely to occur by chance and is considered statistically significant.
8. How do we choose the threshold for determining significance?
The commonly used threshold for determining significance is 0.05. However, the choice of threshold depends on the specific requirements of the analysis and should be based on the context and field of study.
9. Is the p value the only measure of statistical significance?
No, the p value is one of several measures used to determine statistical significance. Other measures, such as confidence intervals and effect sizes, provide additional information about the strength and practical relevance of the relationship.
10. Can a non-significant coefficient have a small p value?
No, a non-significant coefficient is accompanied by a high p value. A small p value indicates statistical significance.
11. Why is it important to consider the p value in relation to the effect size?
The p value tells us about statistical significance, while the effect size provides information about the strength and practical significance of the relationship. Both are important for a comprehensive understanding of the results.
12. Are p values influenced by outliers in the data?
Yes, extreme values or outliers in the data can influence the p value. It is important to analyze and address outliers before drawing conclusions based on the p value.